TERNARY-BINARY ALPHABETIC HYBRID PSK/FH SIGNAL DESIGN FOR LPI RADAR

Volume 118 No. 11 2018, 707-716 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v118i11.91 ijpam.eu TERNARY-BINARY ALPHABETIC HYBRID PSK/FH SIGNAL DESIGN FOR LPI RADAR 1 Shaik Maznu, 2 I.A. Pasha, 3 P. Chandrasekhar Reddy, 4 Ramesh Deshpande 1 V.J.I.T, Dept. of ECE, Aziznagar, Hyderabad, TS- India. 2 B.V.R.I.T, Professor, Dept. of ECE, Narsapur, Medak, T.G- India. 3 JNTUH College of Engineering, Professor Coordinator, Dept. of ECE, Hyderabad, T.G India. 4 B.V.R.I.T, Assoc Professor, Dept. of ECE, Narsapur, Medak, T.G- India. 1 mazunu.shaik@gmail.com, 2 pasha.ia@bvrit.ac.in, 3 drpcsreddy@gmail.com 4 deshpande@bvrit.ac.in Abstract: Joint Ternary-binary interpretation derived from binary phase coded hybrid frequency hop spread signal design for Low Probability Intercept (LPI) radar have good autocorrelation properties. For the purpose of transmission the ternary phases representation can be coded into a binary phased hybrid frequency hop signal. On reception, it can be processed as a binary phased hybrid frequency hop signal; and also be decoded in the form of ternary. Additional advantage accrue through degree of freedom when a zero ternary alphabet is decoded into binary [+ - ] or [- +] alphabet. These two representations provide a coincidence detection technique for efficient target detection for noisy LPI radar waveform. Within the frame work Hamming Scan (HS) algorithm is employed as an optimization technique to improve discrimination Factor (DF). Further improvement in DF is accrued by employing Hamming back-track (HBT) algorithm developed for binary phase coded frequency hop spread signal. Keywords: LPI radar; Hybrid Frequency Hop spread Signal; Discrimination Factor; Hamming Scan. 1. Introduction The waveforms are specifically designed to make detection process very difficult. Such signals are called as low probability intercept (LPI) radar waveforms. The LPI antenna must use a transmit radiation pattern with low side lobes. The low side lobes in transmit radiation pattern reduce possibility of interception and detection of the electronic warning (EW) intercept receiver. Any changes in the radar s signature can help confuse an intercept receiver and make intercept difficult. A large pulse compression ratio that provides a wide band and low peak power used in LPI transmission in order to avoid interception by EW intercept receiver [1]. Barker codes are combined with FH spread signal to achieve a peaky auto correlation function [2]. Further by increasing number of elements or phase values in the sequence, allows designing a longer sequence, resulting peaky auto correlation function with less side lobes [3]. Detection and classification of longer sequence pulse compression signals is a major challenge for EW receiver [4]. To obtained long sequence with peaky autocorrelation is an optimization problem in the field of LPI radar signal design. Earlier research based on ternary sequence for compression radar results into improved performance in terms of achieving high DF/merit factor (MF) [5-7]. The ternary sequence faces two problems [8]. First problem ternary sequence has alphabet zero as an element, which implies no transmission during some time slots. Second problem is it is difficult to have on-off switches at high power in comparison to phase shifting. In [8], authors proposed a ternary sequence that can be coded into a binary sequence for transmission purpose. In the receiver it can be subjected to dual ternary-binary phase representations to facilitate a coincidence detection scheme for efficient target detection. In authors [9] the wigner-ville Hough transform (WVHT) in the detection of linear frequency modulated waveform (LFM) of intercept LPI radar waveform. The periodic WVHT (PWVHT) significantly better performance than WVHT for LFMCW LPI signal was proposed author [9]. In the proposed work the binary phases modulated frequency hop (FH) can be chosen as a LPI signal and thus bi-alphabetic interpretations leads to high DF. In frequency hopping multiple access systems, the average hamming correlation among frequency hopping sequences as well as the maximum hamming correlation is an important performance measure [10-13]. The proposed signal design for LPI radar, the ternary phase representation S t obtained during binary phase coded sequence combined with frequency hop spread signal will be utilized to improve DF values of LPI radar transmitted waveform. However, the ternary phase representation can be coded into binary phase 707

coded S b through the process of substituting binary bigrams i.e. +1 + 1+1, -1-1-1, 0 +1-1 or 0-1+1. This increase in length of the inter pulse modulation code helps in achieving larger pulse compression ratios in LPI radar transmission. Such LPI radar transmitted waveform will be difficult to characterize by the EW intercept receiver. 2. Binary Phase Coded Frequency Hop Spread Spectrum Signal Design A. Binary phase shift Code (BPSK) Increasing the number of elements or phase changes in the sequence allows the design of longer sequences, to result in a pulse compressed radar waveform with low time side lobes and higher range resolution waveform with greater processing gain in the receiver [4]. The Binary phase shift code with phase elements S = {+1, -1}, the element (1) indicates 0 phase and (-1) indicate π radians. B. Frequency Hop (FH) Spread Spectrum Signal Consider a spread signal of period T which is a train of N equal length pulses with each pulse width τ. In order to generate binary phase shift signal (BPSK) consider a binary sequence S and carrier c(t) with τ samples. b(t) = S*c(t); t=1 τ (1) where N is integer The carrier signal will have τ time samples within the carrier cycle. For binary code, where, S Є{1,2 N}. FSK radar using frequency hopping (FH) techniques hops or changes the transmitting frequency in time over wide bandwidth in order to prevent an un wanted receiver from intercepting the waveform. The radar frequency slots are chosen from an FH sequence gives the radar an advantage in terms of processing gain. Since the frequency sequence appears random to the intercept receiver, the possibility of following the changes in frequency is impossible. This prevents a jammer from reactively jamming the transmitted frequency. In FH spread spectrum waveform, the transmitted frequency f j is chosen from the FH sequence{f 1,f 2, f N } of available frequencies for transmission at set of time intervals{t 1,t 2, t N }. To generate FH spread signal, consider M carrier frequencies with τ samples within the carrier cycle 2π, where M is integer. The carrier frequency c(t) =Aexp[j2π f j (t+ф)] (2) where, j=1,2 M Allocation of carrier frequencies for frequency hop spread signal generation is done on random selection basis in various time slots. The Frequency Hop Spread signal is given by p(t)= c(t) (3) Where u(t)={1 0 t T/N (4) 0 otherwise} To obtain frequency Hop spread signal P(t) is ternary representations P(t) Є(+1,0,-1) and its length N t. C. Binary Phase Coded Frequency Hop Spread Spectrum Signal In binary phase coded frequency hop spread spectrum signal design the BPSK signal b(t) is modulated with frequency hop Spread signal P(t). In this process the frequency hop spread signal is modulated with binary phase shift code i.e. each carrier frequency for generation of frequency hop spread signal which is relieved during a specific period of time is combined with BPSK. For this process we have chosen phases 0, π, π/2, 3π/2, 2π, 5π/2 for carrier frequencies for generation of FH signal such that the resultant signal is ternary representation. That ternary representation is modulated with BPSK to obtain mixed ternary phase representations. The mixed ternary representation length is same as the ternary representation length N t. A correlation receiver with a phase mismatched reference signal is used to receive the echo wave of target instead of a perfectly phase matched reference. This allows radar to generate signals that can match targets spectral response in both magnitude and phase. The Combined ternary representation (binary phase coded frequency hop spread spectrum signal) is given by S(t)= b(t)*p(t) (5) The mixed ternary representation S(t) is further decoded into binary phase sequence by using binary bigrams for the purpose of transmission, viz:+1 +1+1, -1-1-1, 0 +1-1 or -1+1. The length (N b ) of the binary bigram sequence S(b) will be double the length of the mixed ternary when coded into binary bigrams. Hence the pulse compression ratio will increase. This is an advantage when electronic warning (EW) receiver attempts to characterize, classify and detect LPI radar transmitted waveform. 3. Design Algorithm For Bi-Alphabetic Phase Representations The notation for design algorithm of bi-alphabetic obtained from binary phase code modulated with frequency hop spread signal is S(t)=[s 0,s 1,s 2,.s Nt-2,s Nt-1 ] (6) S(t) be the intra pulse code length of the hybrid frequency hop signal of length N t, where the element S j are taken from alphabets [+1, 0, -1]. ρ (p) = + (7) ρ (p) is called the a periodic autocorrelation function of the mixed ternary representation. 708

D=ρ (0)/ max ρ (p) (8) where D is the discrimination factor. The transmitted binary phase coded frequency hop signal should be derived from ternary phase representations obtained from binary phase coded frequency hop spread spectrum signal which is a high discrimination factor. When such a binary bigram is transmitted they can be subjected to bi-alphabetic representations at receiver. The element +1 in the ternary representation can be coded as +1 +1 in the binary representation, the element -1 can be coded as -1-1 and the element 0 can be coded as +1-1 or -1 +1 in the transmitted binary representation. When such a bialphabetic phases is subjected to hamming scan (HS) for recursive search, the sum of the discrimination factors d=dt+db can be considered as an objective function to maximize. Here dt is the discrimination factor of combined ternary representation obtained from binary phase coded frequency hop spread spectrum signal and db is the discrimination factor of substituted binary bigrams. 4. Optimization of Bi-Alphabetic Phase Representations The recursive Hamming scan (HS) algorithm is applied to randomly selected binary sequence S Є (+1, -1) when combined with FH spread signal to obtain optimized mixed ternary representation. The proposed coding of mixed ternary sequence is taken into binary representation by substituting a binary bigram, i.e. +1 +1 +1, -1-1 -1 and 0 +1-1 or -1 +1.The mixed ternary sequence has mz zeros, there are 2 mz binary. The best one among them is chosen. In this proposal first the mixed ternary phase representations is optimized after that freedom is offered to 0 elements. When ternary representation is substituted by using binary bigrams the length of the binary bigram representation is increased to double the length of the mixed ternary representation. It is possible to use dual on ternary phase representations so that the two representations are combined together to give better performance without giving any representations individually. Bi-alphabetic hamming scan is adopted for this purpose. Further improved DF values employ Hamming back-track (HBT) algorithm to bi-alphabetic representation. A. Hamming Scan Algorithm For Binary Phase Coded Frequency Hop Spread Spectrum Signal Design The Hamming scan is an algorithm which is more efficient though it is sub-optimal. The Hamming scan looks at all the Hamming neighbors and picks up the one with largest discrimination factor. If it is better than the original sequence, the algorithm is recursively continued from there as long as improvement is possible. The Hamming scan was expedited and made applicable at larger lengths by not calculating the a periodic autocorrelation of the Hamming neighbors ab initio, recognizing the fact that as only one element is mutated, only its difference contribution needed to be taken into account. Each of the elements in the binary phase sequence [+1, -1] can be mutated in two possible ways:+1-1 or -1 +1 resulting is combined to FH spread signal to obtain optimized ternary representation of binary phase coded frequency hop spread spectrum signal. These are two strands of Hamming neighbors. The better neighbor of these two strands could be selected by recursive local search among the Hamming neighbors of resulting binary phase sequence. The same technique is employed to substitute binary bigrams of ternary to obtain good combined discrimination factor. This idea is based on earlier work done for Bi-parental product algorithm for coded waveform design in radar [6] that employed Hamming scan and back-track algorithm for obtaining the ternary sequences with high merit factor. These results are used in the bi-alphabetic pulse compression radar signal design [8]. This idea is employed for the proposed work. The Hamming scan as optimization technique to improve discrimination factor values and further improve implementing a back tracking algorithm for bialphabetic phases. B. BI-Alphabetic Hamming Scan The performance of the binary bigram representations can be further improved if it is subjected to a bialphabetic phases in terms of both ternary-binary phases. In this way an effective coincidence scheme for target detection in which the sum of the discrimination factor of self-contributions because of bi-alphabetic sequence can be taken to maximize joint objective function. The mutation in the binary phase sequence is combined with FH spread signal to obtain optimizing ternary representation. The ternary representations are substituted by binary bigrams that undergo mutation +1-1, -1 +1 to optimize the binary bigrams. The resulting binary bigram representation can be further optimized from 2 mz alternatives as explained in section D. In TABLE I listed optimized with good DF values of ternary representation obtained from Binary Phase Coded Frequency Hop Spread Spectrum signal and optimized binary bigrams sequence with good DF values. The listed values of DF for mixed ternary representation is much better than the DF values of phase coded hybrid waveform design for LPI radar [3]. In phase coded hybrid waveform design for LPI radar. The authors referred more number of carrier frequencies for derivation of FH spread signal to improve DF. In this process the randomly selected binary sequence is optimized using HS algorithm, 709

which is combined with different kinds of carrier frequencies to derive FH spread signal but it is not ternary representation. In the process of mixed ternary representation considering the carrier frequencies with phases 0, π/2, π, 3π/2, 2π, 5π/2 for generation of FH spread signal which is ternary. These ternary representations combined with optimized binary phases using HS algorithm to obtain optimized combined ternary. C. Hamming Back Track Algorithm For Bi- Alphabetic When bi-alphabetic Hamming scan contains no representations with discrimination factor superior to starting representations, the Hamming back-track still looks at the prescribed number n (called span) of the best Hamming neighbor [8]. The algorithm then obtains the best sequence obtainable from them by a prescribed number (called the height) of recursive Hamming scan and selects it, if it is superior to the starting sequence. The ternary representation obtained from Binary phase modulated Frequency Hop Spread Spectrum signals are two strands of Hamming neighbor corresponding to two alphabet value obtained by mutation and n of best neighbor are picked up on each strand. A span of n=6 is used in this proposed work. If the Hamming back-track succeeds improving discrimination factor, the search can resume by further application of bi-alphabetic Hamming scan. Each time the binary bigram representation corresponding to the improved optimization of combined ternary representation is obtainable from binary phase coded frequency hop spread spectrum signal. The values are listed in TABLE II. By applying a back- track algorithm for bialphabetic representation has further improve in the discrimination factor by using degree of freedom algorithm for the ternary representation is explained in section D and its values as shown in TABLE IV. The comparison of sum of DF values of HBT algorithm for ternary-binary alphabetic representation and HBT with DOF is shown in TABLE V. D. Degree of Freedom(DOF) Due To 0 Elements in Ternary The recursive local search among hamming neighbors of a binary phase sequence is modulated with FH spread signal to obtain optimized ternary representation. To build substituted binary bigram representations S b of length 2N t from ternary phase representations of binary phase coded frequency hop spread spectrum signal. During this correspondence the ternary 0 can be coded in two different ways: +1-1 or -1 +1. Thus the binary bigram sequence can be taken from 2 mz alternatives, where mz is the number of zero representation in the ternary of binary phase modulated frequency hop spread spectrum signal. This extra degree of liberty can be explored to take a binary bigram among 2 mz alternatives which has the more discrimination factor. This problem can itself be organized as a selective hamming scan which permits bigram mutation to -1 +1 +1-1 in the binary bigram representation only where these bigrams have an origin due to 0 element in the ternary of binary phase modulated frequency hop spread spectrum signal. 5. Detection Performance At the receiver to detect the target from the coincidence peaks of cross correlation of Ternary phase representations (St) and Binary (Sb) channels. The joint coincidence of cross correlation peaks simultaneously in different channels indicates the presence of target. It is also interesting to observe that the surrounding side lobes will not align or synchronize in three channels. This eliminates the possibility of false target detection due to time side lobes. This is as shown in Fig.4. 6. Discussions The sum of discrimination factor values of bialphabetic phases obtained using Hamming scan and Hamming back-track algorithm for various length of ternary are shown in TABLE III. The corresponding comparison relationship as shown in Fig.1, it is clear that the sum of DF values is improved when Hamming back-track algorithm is used as compared to DF values obtained using Hamming scan algorithm. In reference [3] referred as increases intra pulse width τ of the pulse repetition interval decreases the discrimination factor values like binary phase modulated frequency hop spread spectrum sequence length N=360, DF=5.7 and N=720, DF=3.1 which values obtained for four carrier frequencies i.e. M=4 are used to generate frequency hop spread signal. In the proposed work intra pulse width τ is kept constant, when there is increase number of intra pulses i.e. randomly selected binary increases the discrimination factor values like this S=60, τ=6, M=3, Combined ternary sequence obtained for binary phase coded frequency hop spread signal length N t =360, DF=11.9355 and S=120, τ=6, M=3, N t =720, DF=15.2182 as shown in TABLE I. As the length of the binary increases the pulse compression ratio also increases as shown in Fig.1. The corresponding sum of discrimination factor of bi-alphabetic sequence using HS and HBT algorithm is shown in Fig.1. The comparison of discrimination factors of bi-alphabetic sequence of ternary and binary bigrams using HBT algorithm is shown in Fig.2. The 710

DF values of substituted binary bigram are not more than 2 of 360 to 1440. By applying degree of freedom algorithm to substituted binary bigrams of ternary that values are reaches range from 9 to 11. The values are shown in TABLE IV. The comparison of sum of discrimination factor values of bi-alphabetic sequence of HBT algorithm and HBT with DOF is shown in Fig.3. 7. Conclusion The results shows that the ternary obtained from optimized binary sequence modulated with specially designed FH spread signal i.e. ternary can yield improvement in DF than phase coded hybrid waveform design for LPI radar. This was made possible because zero elements in the ternary, which contribute zero to logged products in the autocorrelation so that only less contributions had to balance each other out. The existence of zero elements possessed technical problem of on/off transmission at high power. If cross correlation is computed after decoding the received signal into discrete, then the ternary can be transmitted after coding it into binary bigram, so that make attempt to characterize the signal by EW intercept receivers. The received signal can be decoded into two significances, (1) a binary, and (2) a ternary. The peaky autocorrelation should then apply to both of them, or, as a compromise, they should be jointly good without giving any significance being best individually. This is new signal design problem and has been solved in two ways in this paper. Length of Ternary phase representations (N t ) Table 1. Sum of DF Values of Bi-Alphabetics Using HS Algorithm. Discrimination Factor Values DF values of Ternary (dt) DF Values of Binary (db) Sum of DF values D=dt+db 180 8.1818 1.8750 10.0658 240 7.5 1.8462 9.3446 300 9.375 1.8519 11.2267 360 10.000 1.9355 11.9355 420 10.000 1.8584 11.8584 480 10.909 1.8462 12.7552 540 11.25 1.8881 13.1381 600 12.00 1.9231 13.9231 660 11.785 1.9527 13.7384 720 13.333 1.8848 15.2182 Length of Ternary phase representations (N t ) Table 2. Sum of DF Values of Bi-Alphabetics Using HBT Algorithm Discrimination Factor Values DF values of Ternary phase representations (dt) DF Values of Binary (db) Sum of DF values D=dt+db 180 8.3059 1.8324 10.1383 240 8.63 1.8462 10.4762 300 10.075 1.8987 11.9737 360 10.508 1.9355 12.4439 420 10.512 1.8750 12.3874 480 12.028 1.8462 13.8750 540 12.246 1.9141 14.1608 600 13.019 1.9231 14.9422 660 13.402 1.9298 15.3319 720 13.994 1.9123 15.9068 711

Table 3. Comparison of Sum of DF Values of Bi-Alphabetics Using HS and HBT Algorithm Length of Ternary phase representations (N t ) Discrimination Factor Values HS(db+dt) HBT(db+dt) 180 10.0658 10.1383 240 9.3446 10.4762 300 11.2267 11.9737 360 11.9355 12.4439 420 11.8584 12.3874 480 12.7552 13.8750 540 13.1381 14.1608 600 13.9231 14.9422 660 13.7384 15.3319 720 15.2182 15.9068 Table 4. Sum of DF Values of Bi-Alphabetics Using HBT and DOF Algorithm Length of Ternary (N t ) Discrimination Factor Values DF values of Ternary (dt) DF Values of Binary (db) Sum of DF values D=dt+db 180 8.3059 11.25 19.5554 240 8.63 10.7120 19.3424 300 10.075 10.0000 20.075 360 10.508 9.2412 19.7496 420 10.512 9.363 19.8753 480 12.028 9.2727 21.3015 540 12.246 9.3103 21.557 600 13.019 9.7143 22.734 660 13.402 9.3462 22.7483 720 13.994 9.6596 23.6541 Table 5. Comparison of Sum of DF Values of Bi-Alphabetics Using Only HBT And HBT and DOF Algorithm Discrimination Factor Values Length of Ternary (N t ) HBT(db+dt) HBTand DOF(db+dt) 180 10.1383 19.5554 240 10.4762 19.3424 300 11.9737 20.075 360 12.4439 19.7496 420 12.3874 19.8753 480 13.8750 21.3015 540 14.1608 21.557 600 14.9422 22.734 660 15.3319 22.7483 720 15.9068 23.6541 712

Sum of Discrimination Factor D=dt+db 16 15 14 13 12 11 10 BFHSS with HS. BFHSS with HBT. 9 100 200 300 400 500 600 700 800 Length of the ternary sequence S(t) Figure 1. Sum of discrimination factor of bi-alphabetics using HBT Algorithm DF of ternary(dt)and binary(db)with HBT 14 12 10 8 6 4 2 DF db with HBT. DF dt with HBT. 0 100 200 300 400 500 600 700 800 Hamming Back Track Algorithm applied seq length Figure 2. Discrimination factor of bi-alphabetics Ternary and Binary phases Using HS and HBT algorithm. Sum of Discrimination Factor D=dt+db 24 22 20 18 16 14 12 BFHSS with HBT. HBT with DOF. 10 100 200 300 400 500 600 700 800 Length of the ternary sequence S(t) Figure 3. Sum of discrimination factor of bi-alphabetics using Only HBT and HBT and DOF algorithm. 713

Figure 4. Coincidence detection of Ternary (St) and Binary (Sb) References [1] Phillip E. Pace, Detecting and Classifying LPI Radar, Artech House, Norwood, 2003. [2] Shaik Mazunu, I. A. Pasha, P. Chandra Sekhar Reddy, Design of Hybrid Binary phase coded frequency hop spread signal for LPI Radar, ICECE 08-2012 Proceedings, PP 44-48. [3] Shaik Mazunu, I. A. Pasha, P. Chandra Sekhar Reddy, Phase Coded Hybrid Waveform Design for LPI Radar, Int. J. on recent trends in Engineering and Technology, Vol.11, No.1, pp. 75-82, July 2014. [4] AK Singh, Dr. K. Subba Rao, Detection, Identification & Classifying of intra pulse modulated LPI Radar Signal Using Digital Receiver, International Journal of Emerging Technology and Advanced Engineering, Volume 2, Issue 9, September 2012. [5] Moharir P S, Maru V M, Singh R, S-K-H algorithm for signal design Electron. Lett. 32:1648-1649, 1996 [6] Moharir P S, Subbarao K, Non binary sequences with superior merit factors, IETE J. Res. 1:49-53, 1997 [7] Moharir P S, Maru V M, Singh R, Simonization for signal Design, Sadhana 23:351-358, 1998 [8] I A Pasha, P S Moharir, N Sudharshan Rao, Bi-alphabetic pulse compression radar signal design, Sadhana,vol.25, Part 5, pp.481-488, October 2000 [9] FRANCIS G.GEROLEO, MATTE BRANDT- PEARCE, Detection and estimation of LFMCW Radar Signals, IEEE Transactions on aerospace and Electronics systems, Vol. 48, No.1 pp. 405-417, Jan 2012. [10] N.C.Beaulieu and D.J.Young, Designing time hopping ultra Wide bandwidth receiver for multiuser interference Environments, Proc.IEEE, vol.97, no.2, pp. 255-284, 2009 [11] Jin-Ho Chung and Kyeongcheol Yang, Frequency Hopping Sequence Sets with low average and maximum Hamming Correlation, Submitted to IEEE transaction on Information theory, July 27, 2011. [12] J.-H. Chung, Y. K. Han, and K. Yang, No-hitzone frequency-hopping sequence sets with optimal Hamming autocorrelation, IEICETrans.Fund. Elec. Commun. Comp. Sci., vol. E93-A, no. 11, pp. 2239-2244,Nov. 2010. [13] C. Ding and J. Yin, Sets Of Optimal- Frequency Hoping Sequences IEEE Trans, Inform, Theory, Vol.54, no.8, PP.3741-3745, Aug.2008 [14] T. Padmapriya and V. Saminadan, Inter-cell Load Balancing technique for multi-class traffic in MIMO-LTE-A Networks, International Journal of Electrical, Electronics and Data Communication (IJEEDC), ISSN: 2320-2084, vol.3, no.8, pp. 22-26, Aug 2015. 714

[15] S.V.Manikanthan and K.srividhya "An Android based secure access control using ARM and cloud computing", Published in: Electronics and Communication Systems (ICECS), 2015 2nd International Conference on 26-27 Feb. 2015,Publisher:IEEE,DOI:10.1109/ECS.2015.7124833. [16] Rajesh, M., and J. M. Gnanasekar. & quot; GCCover Heterogeneous Wireless Ad hoc Networks.& quot; Journal of Chemical and Pharmaceutical Sciences (2015): 195-200. [17] S.V.Manikanthan and D.Sugandhi Interference Alignment Techniques For Mimo Multicell Based On Relay Interference Broadcast Channel International Journal of Emerging Technology in Computer Science & Electronics (IJETCSE) ISSN: 0976-1353 Volume- 7,Issue 1 MARCH 2014. 715

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